A semi-flexible model prediction for the polymerization force exerted by a living F-actin filament on a fixed wall

Abstract

We consider a single living semi-flexible filament with persistence length p in chemical equilibrium with a solution of free monomers at fixed monomer chemical potential µ1 and fixed temperature T . While one end of the filament is chemically active with single monomer (de)polymerization steps, the other end is grafted normally to a rigid wall to mimick a rigid network from which the filament under consideration emerges. A second rigid wall, parallel to the grafting wall, is fixed at distance L << p from the filament seed. In supercritical conditions where monomer density ρ1 is higher than the critical density ρ1c, the filament tends to polymerize and impinges onto the second surface which, in suitable conditions (non-escaping filament regime) stops the filament growth. We first establish the grand-potential Ω(µ1, T, L) of this system treated as an ideal reactive mixture and derive some general properties, in particular the filament size distribution and the force exerted by the living filament on the obstacle wall. We apply this formalism to the semi-flexible, living, over a compression range much narrower than the size d of a monomer. Employing this universal form for living filaments, we find that the average force exerted by a living filament on a wall at distance L is in practice L independent and very close to the value of the stalling force F H s = (kBT /d) ln(ρ1) predicted by Hill, this expression being strictly valid in the rigid filament limit. The average filament force results from the product of the cumulative size fraction

On the properties of a bundle of flexible actin filaments in an optical trap

“…Hence, Footer et al [21] used an optical trap set-up to measure the forces generated by the elongation of a few parallel-growing actin filaments in contact with a rigid microfabricated barrier, equilibrium being established between the bundle polymerization force and the trap restoring force directly proportional to the trap length. We observe that this set up represents in principle a true stable equilibrium state, as long as temperature and free monomer chemical potential are kept fixed and the implied chemical reactions are reversible with no filament escaping laterally along the obstacle wall [4,21,23]. Footer et al monitored the growth of approximately eight actin filaments and found a stationary force significantly smaller than the value predicted by Hill's theory.…”

“…Actin filaments in cells are usually organized into fairly rigid bundles with the help of fascin, an actin cross-linking protein, while their growth is controlled by capping proteins, which prevent them from becoming too long and flexible [1]; due to these features and to the intrinsic large stiffness of these filaments, most of the existing models discard their flexibility and treat them as infinitely stiff. In this paper, following the lines set by [2][3][4], we investigate the role of flexibility in the process of reversible work production by F-actin filaments. Over the last decades, the underlying mechanism which enables cells to produce forces has been extensively studied, both theoretically and experimentally.…”

“…Along these lines, in a simulation approach of filament growth against a constant load [23], flexibility was found to prevent the establishing of a true stationary non-equilibrium state since beyond some length, semi-flexible filaments can loose contact with the wall and grow parallel to it, hence reducing the force they are able to provide. This phenomenon has been called "pushing catastrophe" in the context of constant-load experiments [23] and "escaping filaments" in a study restricted to equilibrium conditions [4].…”

“…We close the section defining the meaning of force measurement in terms of ensemble averaging. In section IV we briefly recall our model of F-actin filaments [2,4] and extend the non-escaping filament regime criteria of ref. [4] to the present case of the optical trap.…”

“…The discrete version of this model (d-WLC) has then been extended to the case of a bundle of independent "living" filaments growing in contact with a rigid fixed wall in a reactive canonical ensemble [3]; within this statistical mechanical description several general features have been derived, namely the equilibrium filament size distribution and the associated average equilibrium force exerted on the opposite wall. Along these lines, a recent study [4] has extended this analysis to the reactive grand canonical ensemble, specified by temperature T , volume V and free monomers chemical potential µ 1 , for a single grafted living semi-flexible filament modeling F-actin, hitting a fixed wall.…”